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# Structural Monte Carlo

#### afterworkguinness

##### Active Member
Hello,
The notes on the Linda Allen reading (Chapter 3) say the difference between a regular Monte Carlo simulation and a Structured Monte Carlo simulation is the structured one can "generate correlated scenarios based on a statistical distribution"

What are correlated scenarios ? Would I be correct in inferring they are scenarios that are related e.g.: increase in domestic interest rate and increase in FX forward price vs simply an increase in the domestic interest rate ?

Thanks and sorry for hogging the forum, I'm finding the Allen chapters to be very dense and somewhat confusing.

(BTW, I did try Google first to no avail)

Cheers

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi afterwork,

The notes refer to Linda Allen 3.2.2. which, frankly, is a terrible (or, dense, as you say) 3-page section of Allen's Chapter 3: it hardly explains MCS. We are near to producing the corresponding learning XLS, but here is last year's https://www.dropbox.com/s/pyvz6d3nugz9ozn/T4.a_2012_XLS_bundle_valueatrisk_v1009.xlsx
(the relevant sheet is "Structured MCS," which is supported by the subsequent sheet called "Cholesky Decomposition")

and the statement in Allen, page 99, is "The main advantage of the use of structured Monte Carlo (SMC) simulation is that we can generate correlated scenarios based on a statistical distribution."

So, without going into great detail, the XLS does basically two things:
1. It assumes a portfolio can be reduced to several risk factors, each risk factor is characterized by a standard random normal. This is the "inverse transformation" where a random uniform is translated into a random standard normal; in EXCEL, =NORM.S.INV(RAND()). As i understand, this step alone would satisfy some definitions of "structured MCS; i.e., the utilization of parametric (normal, in this case) distribution to characterize risk factor returns. Linda Allen, to my knowledge, is not specific, she might by "structured" refer to the second big step illustrated in the XLS:
2. the use of the correlation matrix (and the Cholesky Decomposition) to translate the independent standard random normals into correlated normals
That's all, really. Allen, IMO, summarizes these features when she writes "The scenarios that will be generated using the estimated variance–covariance matrix will be generated based on a set of correlations estimated from real data", and, indeed that, to me, is the essence spreadsheet in two aspects, and the meaning of "structured:"
1. the ability to not just randomize simulations, but randomize parametric distributions (normal, in this case), and then to go beyond a single inverse transformation ...
2. into several random factors which are correlated (i.e., "covariance-variance matrix")
i hope that helps, thanks,

#### afterworkguinness

##### Active Member
Thanks for clearing that up.

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Last edited:

#### Hamam

##### New Member
Subscriber
will this likely be tested on the exam?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@Hamam please note VRM-2 includes LO: "Explain structured Monte Carlo and stress testing methods for computing VaR and identify strengths and weaknesses of each approach"